A new method called "Fluctuation Expansion" has been recently proposed for solving quantum dynamical problems. This method is succesfully applied to the dynamics of expectation values such that not the wave function itself but the expectation values of the position and momentum operator axe taken into consideration and then the expectation value of certain entities depending on position and momentum operators axe expressed via fluctuation expansion. This brings an infinite number of new unknown, fundamental and associate fluctuation terms. The derivatives of expectation values of the position and momentum operators and fluctuation operators axe expressed in terms of these terms again. The resulting infinite set of differential equations and accompanying initial conditions are truncated at certain fluctuation order and then tried to be solved. Here we take a one dimensional time independent Hamiltonian and consider the zeroth and first order truncations. Equations obtained in this way are investigated in the sense of phase space which is defined by the expextation values of the position and momentum operator and the fluctuations entering the truncated equations. We find certain subspaces of the phase space such that there, certain expressions remain constant. This helps us to reduce the dimension of the problem.